The Boundary Value Problem For K-regular Function And For Generalized Regular Function Vectors In Clifford Analysis

The complex analysis method is a powerful tool studying partialdifferential equation.In this paper ,we mainly study a boundary value problemfor a high-order equation in the complex plane and a boundary value problem inclifford analysis about generalized regular function.In the second chapter,we dis-cuss the Riemann boundary value problem with conjugate k-regular function.Inthe third chapter,we study the Riemann boundary value problem of non-normaltype for k-regular function and the theorems of solvability of the problem areobtained.In the last chaper ,we discuss a class of linear and no-linear boundaryvalue problem with conjugate value and a kind of shift for a class of generalizedregular function vectors in clifford Analysis.With the help of of the theory ofthe sungular integral equation and Schauder fixed point theorem ,we prove theexistence and the uniqueness of solution for the above problem.